Measurement of convergence in plane-wave migration

Chad M. Hogan and Gary F. Margrave

ABSTRACT

We have developed a FOCI-driven imaging code that implements a plane-wave migration algorithm. This algorithm produces images that are interpretable with a fraction of the computation time required for a full prestack migration. Additionally, the image may be selectively refined to maximize the benefit of computation time. To guide this refinement, we propose a measure ("residual") of the convergence of the imaging. This method selects a region of the image to monitor. Then within this region, the l 2 norm of the difference between two successive plane-wave stacks normalized by the l 2 norm of the first plane-wave stack is calculated. This residual decreases rapidly while the image is improving and approaches zero as the image approaches its limit. We have implemented this plane-wave code in order to facilitate highly-efficient prestack wave-equation depth migration. Although plane-wave migration is well-known in the seismic community, we intend to use this code as a starting point for future theoretical developments.

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